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Codes and Turbo Codes : IRIS International - Claude Berrou

Codes and Turbo Codes

IRIS International

By: Claude Berrou (Editor)

Paperback Published: 30th August 2010
ISBN: 9782817800387
Number Of Pages: 415

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The IRIS series consists of computer science, computer networks, and telecommunication books intended for students in higher education (first year university to postgraduate degree level, preparation courses, engineering colleges) and professionals.

Each book in the collection reviews a particular aspect of computer science today. The different themes are explored by authors who have taught the subject for several years or, in the case of emerging concepts, by researchers and specialized engineers working on the subject.

Computer science is an extremely broad scientific and technological discipline which is constantly evolving. Not only does the IRIS collection clarify the foundations of the field by proposing reference books, it also presents the most recent developments through more specialized books.

This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. At the crossroads of information theory, mathematics and electronics, channel coding has undergone many developments since Claude Shannon's founding work. From the simple Hamming code (1950) and LDPC codes (1962) to the more recent turbo codes (1993), channel coding has evolved considerably and has incorporated ever more sophisticated concepts, especially the probabilistic processing of information.

The book's main focus is on iteratively decoded algebraic codes, convolutional codes and concatenated codes; it also examines the digital modulation with which channel coding is closely associated, making up the heart of the physical layer of telecommunications systems. The most important theoretical aspects are presented, and the building of codes is detailed. Decoding algorithms are developed and, whenever possible, accompanied by simulation results characteristic of their correcting power.

Codes and Turbo Codes is intended both as an exploration of the domain, a valuable source of information on the many techniques developed since the mid-twentieth century, and as a step towards addressing those problems which are not yet entirely solved. The authors are researchers and lecturers recognized for their expertise in the field of encoding and decoding algorithms and associated circuits.

Contributorsp. v
Forewordp. ix
Introductionp. 1
Digital messagesp. 3
A first codep. 4
Hard input decoding and soft input decodingp. 7
Hard output decoding and soft output decodingp. 11
The performance measurep. 11
What is a good code?p. 15
Families of codesp. 17
Digital communicationsp. 19
Digital Modulationsp. 19
Introductionp. 19
Linear Memoryless Modulationsp. 22
Memoryless modulation with M states (M-FSK)p. 29
Modulations with memory by continuous phase frequency shift keying (CPFSK)p. 31
Structure and performance of the optimal receiver on a Gaussian channelp. 37
Structure of the coherent receiverp. 37
Performance of the coherent receiverp. 42
Transmission on a band-limited channelp. 59
Introductionp. 59
Intersymbol interferencep. 60
Condition of absence of ISI: Nyquist criterionp. 63
Expression of the error probability in presence of Nyquist filteringp. 68
Transmission on fading channelsp. 69
Characterization of a fading channelp. 69
Transmission on non-frequency-selective slow-fading channelsp. 73
Theoretical limitsp. 83
Information theoryp. 83
Transmission channelp. 83
An example: the binary symmetric channelp. 84
Overview of the fundamental coding theoremp. 86
Geometrical interpretationp. 87
Random codingp. 88
Theoretical limits to performancep. 91
Binary input and real output channelp. 91
Capacity of a transmission channelp. 92
Practical limits to performancep. 96
Gaussian binary input channelp. 96
Gaussian continuous input channelp. 97
Some examples of limitsp. 99
Minimum distances requiredp. 100
MHD required with 4-PSK modulationp. 100
MHD required with 8-PSK modulationp. 102
MHD required with 16-QAM modulationp. 104
Bibliographyp. 107
Block codesp. 109
Block codes with binary symbolsp. 110
Generator matrix of a binary block codep. 110
Dual code and parity check matrixp. 112
Minimum distancep. 113
Extended codes and shortened codesp. 114
Product codesp. 115
Examples of binary block codesp. 115
Cyclic codesp. 120
Block codes with non-binary symbolsp. 130
Reed-Solomon codesp. 130
Implementing the encoderp. 132
Decoding and performance of codes with binary symbolsp. 132
Error detectionp. 132
Error correctionp. 134
Decoding and performance of codes with non-binary symbolsp. 143
Hard input decoding of Reed-Solomon codesp. 143
Peterson's direct methodp. 144
Iterative methodp. 151
Hard input decoding performance of Reed-Solomon codesp. 159
Bibliographyp. 160
Appendix: Notions about Galois fields and minimal polynomialsp. 161
Convolutional codes and their decodingp. 167
Historyp. 167
Representations of convolutional codesp. 169
Generic representation of a convolutional encoderp. 169
Polynomial representationp. 172
Tree of a codep. 173
Trellis of a codep. 173
State machine of a codep. 176
Code distances and performancep. 178
Choosing a good codep. 178
RTZ sequencesp. 178
Transfer function and distance spectrump. 180
Performancep. 183
Decoding convolutional codesp. 186
Model of the transmission chain and notationsp. 187
The Viterbi algorithmp. 187
The Maximum A Posteriori algorithm or MAP algorithmp. 192
Convolutional block codesp. 192
Trellis terminationp. 193
Puncturingp. 196
Bibliographyp. 198
Concatenated codesp. 201
Parallel concatenation and serial concatenationp. 203
Parallel concatenation and LDPC codesp. 206
Permutationsp. 208
Turbo crosswordp. 208
Bibliographyp. 211
Convolutional turbo codesp. 213
The history of turbo codesp. 213
Multiple concatenation of RSC codesp. 215
Turbo codesp. 217
Termination of constituent codesp. 221
The permutation functionp. 222
Decoding turbo codesp. 235
Turbo decodingp. 235
SISO decoding and extrinsic informationp. 238
Practical considerationsp. 245
m-binary turbo codesp. 249
m-binary RSC encodersp. 249
m-binary turbo codesp. 101
Analysis toolsp. 256
Theoretical performancep. 256
Asymptotic behaviourp. 256
Convergencep. 259
Bibliographyp. 266
Turbo product codesp. 271
Historyp. 271
Product codesp. 271
Hard input decoding of product codesp. 273
Row-column decodingp. 273
The Reddy-Robinson algorithmp. 274
Soft input decoding of product codesp. 277
The Chase algorithm with weighted inputp. 277
Performance of the Chase-Pyndiah algorithmp. 280
The Fang-Battail algorithmp. 280
The Hartmann-Nazarov algorithmp. 285
Other soft input decoding algorithmsp. 289
Implantation of the Chase-Pyndiah algorithmp. 291
Bibliographyp. 293
LDPC codesp. 297
Principle of LDPC codesp. 297
Parity check codep. 298
Definition of an LDPC codep. 301
Encodingp. 304
Decoding LDPC codesp. 308
Random construction of LDPC codesp. 312
Some geometrical constructions of LDPC codesp. 315
Architecture for decoding LDPC codes for the Gaussian channelp. 318
Analysis of the complexityp. 318
Architecture of a generic node processor (GNP)p. 319
Generic architecture for message propagationp. 322
Combining parameters of the architecturep. 325
Example of synthesis of an LDPC decoder architecturep. 328
Sub-optimal decoding algorithmp. 330
Influence of quantizationp. 333
State of the art of published LDPC decoder architecturesp. 335
Bibliographyp. 337
Turbo codes and large spectral efficiency transmissionsp. 343
Turbo trellis coded modulation (TTCM)p. 343
Pragmatic turbo coded modulationp. 347
Bibliographyp. 357
The turbo principle applied to equalization and detectionp. 359
Turbo equalizationp. 360
Multipath channels and intersymbol interferencep. 360
The equalization functionp. 362
Combining equalization and decodingp. 366
Principle of turbo equalizationp. 369
MAP turbo equalizationp. 372
MMSE turbo equalizationp. 381
Multi-user turbo detection and its application to CDMA systemsp. 396
Introduction and some notationsp. 396
Multi-user detectionp. 397
Turbo CDMAp. 403
Conclusionsp. 405
Bibliographyp. 407
Indexp. 413
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9782817800387
ISBN-10: 2817800389
Series: IRIS International
Audience: General
Format: Paperback
Language: English
Number Of Pages: 415
Published: 30th August 2010
Publisher: Springer Editions
Country of Publication: FR
Dimensions (cm): 23.11 x 15.49  x 1.78
Weight (kg): 0.72